# GDP Deflator vs. Consumer Price Index

##### By David Henderson

While reviewing Robert Gordon’s book *The Rise and Fall of American Growth* for *Regulation*, I found it relevant to dig into the GDP deflator and the Consumer Price Index. The reasons why would take me too far afield.

I knew and know that the CPI still overstates inflation by a substantial annual percentage. But I didn’t know as much about the GDP deflator.

So I looked at the GDP deflator from the first quarter of 1950 to the fourth quarter of 2015, and the CPI in roughly the same period, from February 1950 to January 2016.

GDP Deflator

1950 Q1: 13.49

2015 Q4: 110.29

CPI

Feb. 1950: 23.6

Jan. 2016: 238.1

So now we can compute the annualized growth rate of each.

For GDP Deflator:

13.49(1 + x)^65.75 = 110.29

(1 + x) )^65.75 = 110.29/13.49 = 8.176

65.75ln(1 +x) = ln8.176 = 2.1012

ln(1 + x) = 2.1012/65.75 = 0.03196

1 + x = 1.0325

x = 0.0325

So annualized rate of growth of GDP deflator = 3.25%.

For CPI:

23.61(1 + x)^65.92 = 238.11

(1 + x)^65.92 = 238.11/23.61 = 10.085

65.92ln(1 +x) = ln10.085 = 2.311

ln(1 + x) = 2.311/65.92 = 0.03506

1 + x = 1.0357

x = 0.0357

So annualized rate of growth of CPI = 3.57%.

The difference is about 0.3 percentage points annually.

So if the CPI overstates annual inflation by 0.8 to 0.9 percentage points, then the GDP deflator overstates annual inflation by about 0.3 percentage points less.

Caution: Jeff Hummel tells me that the computers of the GDP deflator regularly reach back and adjust earlier data, unlike the case for the CPI. So take the above with a grain of salt.